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3 years ago

Which of the following has a graph that is a straight line?

Mathematics

1 answer:

Anit [1.1K]3 years ago

8 0

The answer is Equation 2: y = 5x - 4.5
it is a linear equation that the graph is a straight line

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A fisherman traveled in a boat from point N upstream. After having traveled 6 km, he stopped rowing and 2 hour 40 min after firs

Nat2105 [25]

Answer:

The speed of the river's current is 4.5 km/hr.

Step-by-step explanation:

Given : A fisherman traveled in a boat from point N upstream.

After having traveled 6 km, he stopped rowing and 2 hour 40 min after first leaving N, he was brought back to N by the current.

Knowing that the speed of the boat in still water is 9 km/hour

To find : The speed of the river’s current.

Solution :

Let the speed of current = x km/h

Speed of boat = 9 km/h

Thus, the speed in upstream = (9 - x) km/h

Also, the speed in downstream = x km/h (because the boat is stationary in downstream)

Total distance = 6 km ( from N to the point he reached )

Total time = 2 hours 40 minutes

$\text{2 hours 40 minutes}=2\frac{40}{60}=2 \frac{2}{3} \\\\\text{2 hours 40 minutes}=\frac{8}{3} \text{ hours}$

We know, $\text{Time} = \frac{\text{Distance}}{\text{Speed}}$

According to the question,

$\frac{6}{9-x}+\frac{6}{x}=\frac{8}{3}$

Taking LCM and 6 common

$6[\frac{x+9-x}{(9-x)x}]=\frac{8}{3}$

Take 6 to another side,

$\frac{9}{9x-x^2}=\frac{8}{3\times 6}$

Cross multiply,

$9\times 18=8\times(9x-x^2)$

$162=72x-8x^2$

Taking 4 common and cancel out

$4x^2-36x+81=0$

Solve quadratic equation by middle term split,

$4x^2-18x-18x+81=0$

$2x(2x-9)-9(2x-9)=0$

$(2x-9)(2x-9)=0$

$\Rightarrow 2x-9=0$

$\Rightarrow x=\frac{9}{2}=4.5$

Therefore, The speed of the river's current is 4.5 km/hr.

6 0

3 years ago

(50 points)There are x ducks in a pond. The number of swans in the pond is equal to the square root of the number of ducks. If t

RoseWind [281]

there are nine ducks and 3 swans

sqrt of 9 equals 3

3 + 9 = 12

6 0

2 years ago

Read 2 more answers

Verify that [tan(theta) + cot(theta)]^2 = sec^2(theta) + csc^2(theta)

Wittaler [7]

(tanθ + cotθ)² = sec²θ + csc²θ

Expand left side: tan²θ + 2tanθcotθ + cot²θ

Evaluate middle term: 2tanθcotθ = $2*\frac{sin\theta}{cos\theta}*\frac{cos\theta}{sin\theta}$ = 2

⇒ tan²θ + 2+ cot²θ

= tan²θ + 1 + 1 + cot²θ

Apply trig identity: tan²θ + 1 = sec²θ

⇒ sec²θ + 1 + cot²θ

Apply trig identity: 1 + cot²θ = csc²θ

⇒ sec²θ + csc²θ

Left side equals Right side so equation is verified

7 0

2 years ago

Can u please answer this question

Paha777 [63]

One Way:
We can change the mixed number to a decimal for comparing.

$1\frac{1}{4}$ m = $\frac{5}{4}$ m = 1.25 m

1.4 m    > 1.25 m
Darren   >   Luke

Darren's jump was higher by (1.4-1.25) 0.15 m

Or another way change the decimal to a fraction and the mixed to an improper fraction too.

$1\frac{1}{4}$ = $\frac{5}{4}$ (Luke)
1.4 = $\frac{7}{5}$ (Darren)
We need a common denominator to compare
$\frac{5*5}{4*5}$ (Luke)
$\frac{7*4}{5*4}$ (Darren)
$\frac{25}{20}$ (Luke)
$\frac{28}{20}$ (Darren)

$\frac{28}{20} > \frac{25}{20}$
  Darren >    Luke

By:
$\frac{28}{20}$ - $\frac{25}{20}$ = $\frac{3}{20}$
Which is also by 0.15 m
Darren jumps higher and by 0.15 m

3 0

3 years ago

How to I solve this problem?

Arturiano [62]

Answer:

x=3

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers